I mean by using a perfect solid stick long enough and moving it forward and backward can I send information fastest than light ? Can you imagine a solid stick long enough to reach the moon and using it to comunicate with the lunar base. Will be information faster than light? What are the theoretical reason other than technical reason for rules this as impossible?
We should rule that a perfect unelastic solid exist ?

2 Answers
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You give the answer yourself : special relativity forbids any perfectly rigid solid, or more quantitatively, give a bound on the elasticity a solid can have ($Y<\rho c^2$). If you have a real solid, with nonzero elasticity, you can compute the speed of sound within this solid as a function of the elasticity/stiffness (see e.g. on wikipedia for the formula). If you move an end of your big stick faster thant this speed of sound, it will compress the stick, and this deformation will take time to propagate to the other end. This question is one of the many non-working way of making faster than light communications. You have many of them debunked here.

To go into "technical reasons", if your stick is made of atoms, since the atoms see each other through electromagnetic interaction, there is no way the move of a bunch of atoms of your stick propagates to other of atoms faster than the speed of electromagnetic force. Of course, this is a technical reason, which is not valid if your "stick" is made by an exotic material where other forces play a key role (for example out of neutron-star mater, where nuclear force are important), but in this case the violation of relativity would come from the force themselves, which then would allow you to build a (too) stiff material.

No.
Whenever you move a pole, this is what's actually happening: You push one end. The molecules at theis end push the next molecules. These molecules push the next, and so on. It really is a sort of sound wave, with an incredibly small frequency. There is a time lag between molecules pushing each other, which is again very small. If the rod is very long, these time differences will become apparent. So, someone one light-minute away will recieve the message in $14.4$ min, assimung an iron rod ( I got the ratio by dividing the speed of sound in iron by the vacuum speed of light)? The moon is $1.282$ light seconds away, so the rod will send the message in $18$ s. Pretty slow compared to what we have for moon communication (i.e, radio waves &c)

A perfectly inelastic solid cannot theoretically exist for the reason that it causes such paradoxi. If we try to relativistically analyse the perfectly rigid solid from the molecular pount of view, we will get big issues.